Normalizing Flows (NFs) are a recently developed class of density estimators, which aim to transform the distribution of interest \(P_{\mathbf {x}}\)  to some tractable base distribution \(P_{\mathbf {z}}\) . Using the change of variables formula, this allows for exact likelihood computation, which is in contrast to other deep generative models such as Variational Autoencoders [1]} or Generative Adversarial Networks [2]}. Impressive estimation results, especially in the field of natural image generation, have lead to great popularity of these deep generative models. Motivated by this success, much effort has been put into the development of new parametric classes of NFs to make them even more performant [3]}, [4]}, [5]}, [6]}, [7]}. However, our theoretical understanding has not developed at the same speed, which, so we claim, slows down further progress in the development of powerful NF architectures.
